2 Answers
2

The negation of "All x are y" is "There is at least one x which is not y".

So, Epimenides is a liar. Therefore his statement "All Cretans are liars" is false. This means that not all Cretans are liars. This means that at least one Cretan tells the truth. He can still be a liar, there just has to be at least one Cretan who's not a liar.

It is not written that the state of being a liar can't change in time. So we can find recursive solution to the problem.

Stage 1: All Cretans are liars, including Epidemides. None of them has ever told a truth.

Stage 2: Epimenides says, that all Cretans are liars. This is a truth, but then, first time in his life, he has told the truth, therefore he isn't a liar anymore.

Stage 3: If Epidemes would say that once again, it would not be truth anymore, because Epidemes is no longer a liar. However, since he is already contaminated with truth, he is no liar anymore, so that statement is a lie.

It is the consequence of start condition, that the liar is someone who have never told a truth. If you allow, that liar tells a truth from time to time, that statement could, as well, be correct from the beginning.